Download H.Wk Booklet Electric Mag Fields (3)

6
Yr. 13 Physics
Magnetic Fields,
Grade boundaries:
 A 75%
 B 65%
 C 55%
 D 50%
 E 45%
Grade
Magnetic Fields
Magnetic Fields & Moving Charges
Magnetic Fields & Moving Charges
Generating
Transformers
%
Magnetic Fields and recap
In experiments to pass a very high current through a gas, a bank of capacitors of total capacitance 50
F is charged to 30 kV. If the bank of capacitors could be discharged completely in 5.0 ms
what would be the mean power delivered?
1
A
9.0 MW
B
4.5 MW
C
110 kW
D
22 kW
Fig. 5.1 shows a rigid, straight metal rod XY placed perpendicular to a magnetic field. The
magnetic field is produced by two magnets that are placed on a U-shaped steel core. The steel
core sits on a digital balance.
X
S
steel core
.
magnets
Y
A
Balance
Fig. 5.1
The weight of the steel core and the magnets is 2.500 N. The rod is clamped at points X and Y.
The rod is connected to a battery, switch and ammeter as shown in Fig. 5.1. The direction of the
magnetic field is perpendicular to the rod.
Switch S is closed.
(a) State the direction of the force that now acts on the rod due to the magnetic field.
.............................................................................................................................................. [1]
(iii) State how you determined the direction of the force.
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.............................................................................................................................................. [1]
–2
(iv) The length of the rod in the magnetic field is 5.0 × 10 m and the current in the rod is 4.0 A.
Assume that the magnets provide a uniform magnetic field of magnetic flux density 0.080T.
Calculate the force acting on the rod due to the magnetic field.
force = ...................................................... N [1]
(ii)
State and explain the new reading on the balance.
reading on balance = ........................................................... N
...........................................................................................................................................
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...........................................................................................................................................
...................................................................................................................................... [3]
(d) The rod is replaced by another rod of the same material having half the diameter of the first
wire and the same length. The potential difference across this rod is the same. Calculate the
force on this rod due to the magnetic field.
force = ...................................................... N [3]
[Total: 9]
.
Figure 5 shows a horizontal wire, held in tension between fixed points at P and Q. A short
section of the wire is positioned between the pole pieces of a permanent magnet, which
applies a uniform horizontal magnetic field at right angles to the wire. Wires connected to a
circuit at P and Q allow an electric current to be passed through the wire
(a) (i) State the direction of the force on the wire when there is a direct current from P
to Q, as shown in Figure 5.
............................................................................................................................................ [1]
(ii) In a second experiment, an alternating current is passed through the wire.
Explain why the wire will vibrate vertically.
...........................................................................................................................................
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............................................................................................................................................ [3]
(b) (i) The permanent magnet produces a uniform magnetic field of flux density 220
mT over a 55 mm length of the wire. Show that the maximum force on the wire is
about 40 mN when there is an alternating current of rms value 2.4 A in it.
[3]
(ii) State the effect of increasing the magnetic flux density of the uniform magnetic
field shown in figure 5.
...............................................................................................................................................
.............................................................................................................................................. [1]
(ii) State the effect of rotating the wire PQ through 90 degrees, such that it lies
parallel to magnet, NS
...........................................................................................................................................
............................................................................................................................................ [1]
(c) The length of PQ is 0.40m. When the wire is vibrating, transverse waves are
propagated along the wire at a speed of 64 ms-1. Explain why the wire is set into
large amplitude vibration when the frequency of the a.c. supply is 80Hz.
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............................................................................................................................................ [3]
Total [12]
Synoptic task
Research how the SI unit of the amp is defined and measured. Produce a
report on this. Cite your sources
Describe an experiment that you could do in a laboratory to use this method
to determine the capacitance of a capacitor . You should suggest
approximate values of any measurements so that you can ensure that your
equipment will have the appropriate sensitivity
Magnetic Fields & Moving Charges 1
1
Fig. 3.1 shows part of an accelerator used to produce high-speed protons. The protons
pass through an evacuated tube that is shown in the plane of the paper.
path of protons
R
evacuated tube
in the plane of
the paper
centre of circle
for path of the
protons
Fig. 3.1
The protons are made to travel in a circle of radius R by a magnetic field of flux density B.
(d) State clearly the direction of the magnetic flux density B that produces the circular
motion of the protons.
............................................................................................................................................
. [1]
(ii) Show that the relationship between the velocity v of the protons and the radius R is
given by v = BQRm where Q and m are the charge and mass of a proton respectively.
[1]
(a) Calculate the magnetic flux density B of the magnetic field needed to keep protons in a
–8
circular orbit of radius 0.18 m. The time for one complete orbit is 2.0 × 10 s.
B = .................................................T [3]
(i)
Explain why the magnetic field does not change the speed of the protons.
...................................................................................................................................................
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............................................................................................................................................. [2]
[Total: 7]
2
(a) Fig. 2.2 shows the path of a positive ion of oxygen-16 inside a mass spectrometer.
region of
magnetic
field
oxygen-16
ion
r
Fig. 2.2
The shaded area in Fig. 2.2 represents a region of uniform magnetic field of flux density 0.14
T. The direction of the magnetic field is out of the plane of the paper. The ion has a speed of
6
–1
4.5 × 10 m s and it enters the region at right angles to the magnetic field. While the ion is
in the magnetic field, it describes a circular arc of radius r. The force experienced by the ion
–13
in the magnetic field is 2.0 × 10
N.
(i)
Calculate the charge Q of the ion.
Q = .......................................................C [2]
(ii) The mass of the ion is 2.7 × 10
–26
kg. Calculate the radius r of the circular path.
r = ..................................................... m [3]
(iii)
In Fig. 2.2, the oxygen-16 ion is replaced by an oxygen-18 ion. The oxygen-18 ion has
the same speed and charge. Explain why this ion describes an arc of greater radius.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
............................................................................................................................................ [2]
[Total: 7]
3
Fig. 3.1 shows a section through a mass spectrometer.
Fig. 3.1
A beam of positive lithium ions enter the evacuated chamber through the hole at X. The ions
travel through a region of uniform magnetic field. The magnetic field is directed vertically into the
plane of the diagram. The ions exit and are detected at Y.
(a) Name the rule that may be used to determine the direction of the force acting on the ions.
.............................................................................................................................................. [1]
(b) Explain why the speed of the ions travelling from X to Y in the magnetic field does not
change despite the force acting on the ions.
...................................................................................................................................................
...................................................................................................................................................
.............................................................................................................................................. [1]
5
–1
(e) The lithium-7 ions are detected at Y. All the ions have the same speed, 4.0 × 10 m s and
–19
charge, + 1.6 × 10
C. The radius of the semi-circular path of the ions in the magnetic
–26
field is 0.15 m. The mass of a lithium-7 ion is 1.2 × 10
kg.
(iii) Calculate the force acting on a lithium ion as it moves in the semi-circle.
force = .......................................................N [2]
(b) Calculate the magnitude of the magnetic flux density B.
B = ...................................................... T [2]
(ii)
–9
The current recorded by the detector at Y is 4.8 × 10 A. Calculate the number of
lithium-7 ions reaching the detector per second.
number per second = ................................................... s
–1
[2]
(d) Fig. 3.2 shows the variation of current I in the detector with magnetic flux density B.
I / 10
–9
5
A
lithium-7 ions
A
0
B
Fig. 3.2
The peak A is due to ions of another isotope of lithium. These ions have the same speed and
charge as the lithium-7 ions. Explain the significance of the ‘height’ and position of peak A.
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[Total: 10]
Magnetic Fields & Moving Charges 2
1
Fig. 2.1 shows the circular path described by a helium nucleus in a region of uniform magnetic
field in a vacuum.
region of uniform
magnetic field
A
B
Fig. 2.1
The direction of the magnetic field is perpendicular to the plane of the paper. The magnetic flux
density of the magnetic field is 0.20 mT. The radius of the circular path is 15 cm. The helium
–19
–27
nucleus has charge + 3.2 × 10
C and mass 6.6 × 10
kg.
(a) Explain why the helium nucleus
travels in a circular path
...........................................................................................................................................
...................................................................................................................................... [1]
(ii)
has the same kinetic energy at A and B.
...........................................................................................................................................
...........................................................................................................................................
...................................................................................................................................... [1]
(b) Calculate the magnitude of the momentum of the helium nucleus.
momentum = ............................................ kg m s
–1
[3]
(c) Calculate the kinetic energy of the helium nucleus.
kinetic energy = ....................................................... J [2]
(ii) A uniform electric field is now also applied in the region shaded in Fig. 2.1. The direction of
this electric field is from left to right. Describe the path now followed by the helium nucleus
in the electric and magnetic fields.
...................................................................................................................................................
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.............................................................................................................................................. [2]
[Total: 9]
2. The Large Hadron Collider (LHC) uses magnetic fields to confine fast-moving charged
particles travelling repeatedly around a circular path. The LHC is installed in an underground
circular tunnel of circumference 27 km.
(a) In the presence of a suitably directed uniform magnetic field, charged particles move at
constant speed in a circular path of constant radius. By reference to the force acting on the
particles, explain how this is achieved and why it happens.
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(b) (i) The charged particles travelling around the LHC may be protons. Calculate the
centripetal force acting on a proton when travelling in a circular path of circumference 27 km
at one-tenth of the speed of light. Ignore relativistic effects.
Force = …………….. N [3]
(b) (ii) Calculate the flux density of the uniform magnetic field that would be required to
produce this force. State an appropriate unit.
answer = …………….. unit ……….. [3]
(c) The speed of the protons gradually increases as their energy is increased by the LHC.
State and explain how the magnetic field in the LHC must change as the speed of the protons
is increased.
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.............................................................................................................................................. [2]
Total [12]
Generating
1.
(a) Define magnetic flux.
...................................................................................................................................................
............................................................................................................................................ [1]
–3 2
(b) Fig. 4.1 shows a generator coil of 500 turns and cross-sectional area 2.5 × 10 m placed
in a magnetic field of magnetic flux density 0.035 T. The plane of the coil is perpendicular to
the magnetic field.
axis of rotation
coil of
500 turns
magnetic field
perpendicular
to paper
Fig. 4.1
Calculate the magnetic flux linkage for the coil in this position. Give a unit for your answer.
magnetic flux linkage = ........................ unit ....................... [3]
(c) The coil is rotated about the axis in the direction shown in Fig. 4.1.
Fig. 4.2 shows the variation of the magnetic flux φ against time t as the coil is rotated.
10
φ
/ 10
–5
8
Wb
6
4
2
0
0
0.01
0.02
0.03
t/s
–2
–4
–6
–8
–10
Fig. 4.2
(i)
Explain why the magnitude of the magnetic flux through the coil varies as the coil
rotates.
...........................................................................................................................................
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...........................................................................................................................................
.................................................................................................................................... [2]
(ii)
State Faraday’s law of electromagnetic induction.
.........................................................................................................................................
................................................................................................................................... [1]
(iv)
Use Fig. 4.2 to describe and explain the variation with time of the induced e.m.f. across the
ends of the coil.
...........................................................................................................................................
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...........................................................................................................................................
.................................................................................................................................... [3]
(v)
Use Fig. 4.2 to determine the magnitude of the average induced e.m.f. for the coil between the
times 0 s and 0.005 s.
average e.m.f. = ..................................................... V [2]
(v)
State and explain the effect on the magnitude of the maximum induced e.m.f. across the ends of
the coil when the coil is rotated at twice the frequency.
...........................................................................................................................................
...........................................................................................................................................
.................................................................................................................................... [2]
[Total: 14]
2
(a) State Faraday’s law of electromagnetic induction.
...................................................................................................................................................
.............................................................................................................................................. [1]
(b) Fig. 5.1 shows a magnet being moved towards the centre of a flat coil.
flat coil
moving magnet
N
S
Fig. 5.1
A current is induced in the coil. Use ideas about energy conservation to state and explain
the polarity of the face of the coil nearer the magnet.
...................................................................................................................................................
...................................................................................................................................................
.............................................................................................................................................. [1]
(c) Fig. 5.2 shows the magnetic field from the north pole of a vertically held bar magnet.
vertical bar
magnet
N
coil at position A
X
Y
coil at position B
Fig. 5.2
(iii) A small flat coil is placed at A. The coil is moved downwards from position A to position
B. The plane of the coil remains horizontal between these two positions. Explain why
there is no induced e.m.f. across the ends of the coil.
...........................................................................................................................................
...........................................................................................................................................
...................................................................................................................................... [1]
(v)
Fig. 5.3 is a graph showing how the magnetic flux density B varies along the horizontal line XY in
Fig. 5.2.
B
0
0 2 4 6 8 10 12 distance from X / cm
Fig. 5.3
E
+
0
0
2
4
6
8
10
12 distance from X / cm
–
Fig. 5.4
The same small flat coil from (i) is moved at a constant speed from X to Y. The plane of the coil
remains horizontal between X and Y.
On the axis provided in Fig. 5.4, sketch a graph to show the variation of the induced
e.m.f. E across the ends of the coil with distance from X.
[3]
[Total: 6]
Transformers
1
(a) Define electromotive force.
...................................................................................................................................................
.............................................................................................................................................. [1]
(i)
Define magnetic flux.
...................................................................................................................................................
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.............................................................................................................................................. [1]
(c) Fig. 1.1 shows a simple transformer.
soft iron core
np
ns
primary
coil
output
secondary
coil
Fig. 1.1
3
The primary coil is connected to an alternating voltage supply. Explain how an e.m.f. is
induced in the secondary coil.
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...........................................................................................................................................
...........................................................................................................................................
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...................................................................................................................................... [3]
(e)
State how you could change the transformer to increase the maximum e.m.f. induced in the
secondary coil.
...........................................................................................................................................
...........................................................................................................................................
...................................................................................................................................... [1]
(i)
A transformer with 4200 turns in the primary coil is connected to a 230 V mains supply. The
e.m.f. across the output is 12 V. Assume the transformer is 100% efficient.
Calculate the number of turns in the secondary coil.
number of turns = ......................................................... [2]
(iii) The transformer output terminals are connected to a lamp using leads that have a total
resistance of 0.35 Ω. The p.d. across the lamp is 11.8 V. Calculate
1 the current in the leads connected to the lamp
current = ...................................................... A [2]
2
the power dissipated in the leads.
power = ..................................................... W [2]
[Total: 12]
2
(a) Define magnetic flux.
...................................................................................................................................................
.............................................................................................................................................. [2]
(b) Fig. 3.1 shows an experiment to demonstrate electromagnetic induction.
X
magnetic
field lines
from solenoid
–
+
d.c. supply
Fig. 3.1
The solenoid is connected to a variable voltage d.c. supply. A coil X is placed close to one
end of the solenoid. The current in the solenoid is reduced. Fig. 3.2 shows the consequent
variation of the magnetic flux density B at right angles to the plane of the coil X with time t.
2.0
B / 10
–2
T
1.0
0
0
1.0
2.0
3.0
t/s
Fig. 3.2
The coil X has radius 3.2 cm and 180 turns.
(i) Explain why the induced e.m.f. across the ends of the coil has a constant value from t =
0 s to t = 2.5 s.
...........................................................................................................................................
...........................................................................................................................................
...................................................................................................................................... [1]
(ii) Calculate the magnitude of the induced e.m.f. across the ends of coil X from t = 0 s to
t = 2.5 s.
e.m.f. = ......................................................V [3]
(c) Fig. 3.3 shows a transformer circuit.
soft iron core
1000 turns
25 turns
15 W lamp
alternating
current
supply
Fig. 3.3
The primary coil has 1000 turns and the secondary coil 25 turns. A lamp is connected to the
output of the secondary coil. The potential difference across the lamp is 6.0 V and the lamp
dissipates 15 W. The transformer has an efficiency of 100%.
(i)
Calculate the current in the primary coil.
current = ......................................................A [2]
(ii)
The alternating voltage supply is replaced by a battery. Explain why the p.d. across the lamp
is zero some time after the battery is connected.
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............................................................................................................................................ [1]
[Total: 9]
Electric Fields
Generating
Magnetic Fields
Magnetic Fields and Moving Charges 1
2
Magnetic Fields and Moving Charges 2
Transformers